广西师范大学学报（自然科学版） ›› 2019, Vol. 37 ›› Issue (4): 86-93.doi: 10.16088/j.issn.1001-6600.2019.04.011

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有限维空间中广义混合变分不等式的近似-似投影算法

王佳玉   

  1. 四川师范大学数学科学学院,四川成都610068
  • 收稿日期:2018-09-11 出版日期:2019-10-25 发布日期:2019-11-28
  • 通讯作者: 王佳玉(1993—), 男, 四川绵阳人,四川师范大学教师。 E-mail:1058380869@qq.com
  • 基金资助:
    国家自然科学基金(11271274);四川自然科学基金(2018JY0201)

Proximate Projected-Like Method for Solving Generalized Mixed Variational Inequalities in Finite Dimension Spaces

WANG Jiayu   

  1. School of Mathematical Sciences, Sichuan Normal University, Chengdu Sichuan 610068
  • Received:2018-09-11 Online:2019-10-25 Published:2019-11-28

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摘要： 本文利用似距离泛函和似投影算子, 在有限维空间中建立了一类广义混合变分不等式的近似-似投影算法,证明了迭代序列是良定的, 在集值映像T为伪单调且上半连续、f是下半连续真凸的条件下证明了迭代序列收敛于广义混合变分不等式的解。

关键词: 广义混合变分不等式, 似投影算法, 似距离泛函, 伪单调映像

Abstract: In this paper,with the adoption of the proximate functional and proximate projection method proposed by Auslender and the establishment of the proximal projection-like method for solving generalized mixed variational inequalities in finite dimension spaces, two results are obtained. Firstly, the iterative sequence is well-defined. Then, every accumulation point of the sequence is a solution of generalized mixed variational inequalities under the condition that the set-valued mapping is pseudo-monotone mapping with upper semi-continuity and f is the lower semi-continuity true convex.

Key words: generalized mixed variational inequalities, projected-like method, proximate functional, pseudomonotone

中图分类号: 

  • O22
[1] SOLODOV M V,SVAITER B F. A new projection method for variational inequality problems[J].SIAM Journal on Control and Optimization, 1999,37(3):765-776.
[2] AUSLENDER A,TEBOULLE M. Projected subgradient menthods whth non-eucliden distances for non-differentiable convex minimization and variational inequalities[J].Mathematical Programming, 2009,120(1):27-48.DOI:10.1007/s10107-007-0147-z.
[3] SALMON G,STRODIOT J J. A bundle method for solving variational inequalities[J].SIAM Journal on Control and Optimization, 2004,14(3):869-893. DOI:10.1137/s1052623401384096.
[4] DING X P,YAO J C,ZENG L C. Existence and algorithm of solutions for generalized strongly nonlinear mixed variational-like inequalities in Banach spaces[J].Computers and Mathematics with Applications, 2008,55(4):669-679.DOI:10.1016/j.camwa.2007.06.004.
[5] DING X P,WANG Z B. The auxiliary principle and an algorithem for a system of generalized set-valued mixed variational inequality in Banach spaces[J].Journal of Computational and Applied Mathematics,2010,233(11):2876-2883. DOI:10.1016/j.cam.2009.11.033.
[6] YAO J C. Existence of generalized variational inequalities[J].Operations Research Letters, 1994,15(1):35-40.
[7] ROCKFELLAR R T. Monotone operators and the proximal point algorith[J].SIAM Journal on Control and Optimization,1976,14:877-898.
[8] HUE TT,STRODIOT J J,NGUYEN V H. Convergence of the approximate peturbed auxiliary problem methods to solve Generalized variational inequalities[J].Journal of Optimization Theory & Applications,2004,121:119-145. DOI:10.1023/b:jota.0000026134.57920.e1.
[9] AUSLENDER A,TEBOULLE M. Interior projection-like methods for monotone variational inequalities[J]. Mathematical Programming,2005,104:39-68.DOI:10.1007/s10107-004-0568-x.
[10]DING X P,TAN K K. A minimax inequality with application to existhce of equilibrium point and fixed point theorems[J].Colloquium Mathematicum, 1992,63(2):233-247.DOI:10.4064/cm-63-2-233-247.
[11]AUBIN J P,EKELAND I. Applied nonlinear analysis[M].New York: Wiley,1984. DOI:10.1016/c2013-0-11033-1.
[12]POLYAK B T. Introduction to optimization[M]. New York:Optimization Software Inc, 1987.
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